Problem: Simplify. Rewrite the expression in the form $z^n$. $\dfrac{z^{7}}{z^{-14}}=$
Solution: Recall that $\dfrac{x^n}{x^m}=x^{n-m}$. $\begin{aligned} \dfrac{z^{7}}{z^{-14}}&=z^{7-(-14)} \\\\ &= z^{7+14} \\\\ &= z^{21} \end{aligned}$